Analytical model for low-frequency transmission loss calculation of membranes loaded with arbitrarily shaped masses

Langfeldt, F., Gleine, W. and Von Estorff, O. (2015) Analytical model for low-frequency transmission loss calculation of membranes loaded with arbitrarily shaped masses. Journal of Sound and Vibration, 349, 315-329. (doi:10.1016/j.jsv.2015.03.037).

Record type: Article

Abstract

An analytical model for the transmission loss calculation of thin rectangular and circular membranes loaded with rigid masses of arbitrary shape, the so-called membrane-type acoustic metamaterials, is presented. The coupling between the membrane and the added masses is introduced by approximating the continuous interaction force with a set of discrete point forces. This results in a generalized linear eigenvalue problem that is solved for the eigenfrequencies and eigenvectors of the coupled system. The concept of the effective surface mass density is employed to calculate the low-frequency transmission loss using the obtained eigenpairs. The proposed model is verified using numerical data from a finite element model and the convergence behavior of the point matching approach is investigated using Richardson extrapolation. Finally, a method based upon the grid convergence index for estimating the error that is introduced due to the point matching approach is presented.

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